Speaker John A. Boehner entered the fray over possible changes to the Senate filibuster rules Thursday, saying bills passed by the Senate after such a change and without GOP support “would be dead on arrival” in his chamber.

“Senate Democrats’ attempt to break Senate rules in order to change Senate rules is clearly designed to marginalize Senate Republicans and their constituents while greasing the skids for controversial partisan measures,” the Ohio Republican said in a statement. “I question the wisdom of this maneuver, especially at a time when cooperation on Capitol Hill is critical, and fully support Leader McConnell’s efforts to protect minority rights, which are an essential part of our constitutional tradition.”

Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., have battled this week over the prospect that Reid could use a procedural device, which supporters call a “constitutional option” and detractors call a “nuclear option,” to change the Senate’s rules with a simple majority vote at the start of the new Congress in January.

The procedural maneuver would prevent Republicans from mounting a filibuster of the rules changes. A two-thirds supermajority is required under existing rules to cut off debate on a change to the standing rules. Some veteran Senate Democrats are uneasy with the idea because even though the changes supported by Reid may be relatively narrow, the controversial simple majority vote could set a new precedent that permits more significant changes in the future.

Aides suggested, however, that Reid and McConnell could negotiate an agreement to avoid a potentially toxic standoff.

Boehner’s entry into the debate carries with it a certain irony, however. The House is a traditionally majoritarian body where the speaker, regardless of party, keeps a tight grasp on floor operations.

House Republicans would be hard-pressed to actually follow through on the threat made in Boehner’s statement. In suggesting that no bills could advance through the House after forcing through such a rules change, Boehner is almost promising a halt in all House-Senate relations, which would only increase the dysfunction on Capitol Hill.